A137330 a(n) = primorial(k) - prime(n) where k is the smallest number for which prime(n) <= primorial(k).

0, 3, 1, 23, 19, 17, 13, 11, 7, 1, 179, 173, 169, 167, 163, 157, 151, 149, 143, 139, 137, 131, 127, 121, 113, 109, 107, 103, 101, 97, 83, 79, 73, 71, 61, 59, 53, 47, 43, 37, 31, 29, 19, 17, 13, 11, 2099, 2087, 2083, 2081, 2077, 2071, 2069, 2059, 2053, 2047, 2041

Offset

1,2

Comments

Does each prime number appear in this sequence at least once?

Answer to previous: Neither 2 nor 5 will appear, as no prime > 5 can end in a 5 or be even. - Bill McEachen, Dec 05 2020

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(6) = primorial(3) - prime(6) = 30-13 = 17.

Mathematica

Block[{a = {}, P = 2, j = 1}, Do[AppendTo[a, If[# > P, j++; P *= Prime[j], P] - #] &@ Prime[n], {n, 57}]; a] (* Michael De Vlieger, Dec 07 2020 *)

Prog

(PARI) a(n) = {my(pp=2, k=1, p=prime(n)); while (pp < p, k++; pp*=prime(k)); pp-p; } \\ Michel Marcus, Dec 06 2020

Crossrefs

Cf. A000040, A002110, A136437.

Sequence in context: A027477 A260780 A243769 * A270277 A271605 A270220

Adjacent sequences: A137327 A137328 A137329 * A137331 A137332 A137333

Keyword

easy,nonn

Author

Ctibor O. Zizka, Apr 07 2008

Status

approved